A Kinematic Evolution Equation for the Dynamic Contact Angle and some Consequences

We investigate the moving contact line problem for two-phase incompressible flows with a kinematic approach. The key idea is to derive an evolution equation for the contact angle in terms of the transporting velocity field. It turns out that the resulting equation has a simple structure and expresses the time derivative of the contact angle in terms of the velocity gradient at the solid wall. Together with the additionally imposed boundary conditions for the velocity, it yields a more specific form of the contact angle evolution. Thus, the kinematic evolution equation is a tool to analyze the evolution of the contact angle. Since the transporting velocity field is required only on the moving interface, the kinematic evolution equation also applies when the interface moves with its own velocity independent of the fluid velocity. We apply the developed tool to a class of moving contact line models which employ the Navier slip boundary condition. We derive an explicit form of the contact angle evolution for sufficiently regular solutions, showing that such solutions are unphysical. Within the simplest model, this rigorously shows that the contact angle can only relax to equilibrium if some kind of singularity is present at the contact line. Moreover, we analyze more general models including surface tension gradients at the contact line, slip at the fluid-fluid interface and mass transfer across the fluid-fluid interface.Comment: 25 pages, 6 figures; accepted manuscript

On a Class of Energy Preserving Boundary Conditions for Incompressible Newtonian Flows

We derive a class of energy preserving boundary conditions for incompressible Newtonian flows and prove local-in-time well-posedness of the resulting initial boundary value problems, i.e. the Navier-Stokes equations complemented by one of the derived boundary conditions, in an Lp-setting in domains, which are either bounded or unbounded with almost flat, sufficiently smooth boundary. The results are based on maximal regularity properties of the underlying linearisations, which are also established in the above setting.Comment: 53 page

ZA production in vector-boson scattering at next-to-leading order QCD

Cross sections and differential distributions for ZA production in association with two jets via vector boson fusion are presented at next-to-leading order in QCD. The leptonic decays of the Z boson with full off-shell effects and spin correlations are taken into account. The uncertainties due to different scale choices and pdf sets are studied. Furthermore, we analyze the effect of including anomalous quartic gauge couplings at NLO QCD.Comment: 10 pages, 11 figure

Simulating and detecting artificial magnetic fields in trapped atoms

A Bose-Einstein condensate exhibiting a nontrivial phase induces an artificial magnetic field in immersed impurity atoms trapped in a stationary, ring-shaped optical lattice. We present an effective Hamiltonian for the impurities for two condensate setups: the condensate in a rotating ring and in an excited rotational state in a stationary ring. We use Bogoliubov theory to derive analytical formulas for the induced artificial magnetic field and the hopping amplitude in the limit of low condensate temperature where the impurity dynamics is coherent. As methods for observing the artificial magnetic field we discuss time of flight imaging and mass current measurements. Moreover, we compare the analytical results of the effective model to numerical results of a corresponding two-species Bose-Hubbard model. We also study numerically the clustering properties of the impurities and the quantum chaotic behavior of the two-species Bose-Hubbard model.Comment: 14 pages, 9 figures. Published versio

Strong Well-Posedness for a Class of Dynamic Outflow Boundary Conditions for Incompressible Newtonian Flows

Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier-Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the outlet. As a key building block for the analysis of such problems, we consider the Stokes equations with such dynamic outflow boundary conditions in a halfspace and prove the existence of a strong solution in the appropriate Sobolev-Slobodeckij-setting with $L_p$ (in time and space) as the base space for the momentum balance. For non-vanishing stress contribution in the boundary condition, the problem is actually shown to have $L_p$-maximal regularity under the natural compatibility conditions. Aiming at an existence theory for problems in weakly singular domains, where different boundary conditions apply on different parts of the boundary such that these surfaces meet orthogonally, we also consider the prototype domain of a wedge with opening angle $\frac{\pi}{2}$ and different combinations of boundary conditions: Navier-Slip with Dirichlet and Navier-Slip with the dynamic outflow boundary condition. Again, maximal regularity of the problem is obtained in the appropriate functional analytic setting and with the natural compatibility conditions.Comment: 31 pages, 1 figur

A multigrid perspective on the parallel full approximation scheme in space and time

For the numerical solution of time-dependent partial differential equations, time-parallel methods have recently shown to provide a promising way to extend prevailing strong-scaling limits of numerical codes. One of the most complex methods in this field is the "Parallel Full Approximation Scheme in Space and Time" (PFASST). PFASST already shows promising results for many use cases and many more is work in progress. However, a solid and reliable mathematical foundation is still missing. We show that under certain assumptions the PFASST algorithm can be conveniently and rigorously described as a multigrid-in-time method. Following this equivalence, first steps towards a comprehensive analysis of PFASST using block-wise local Fourier analysis are taken. The theoretical results are applied to examples of diffusive and advective type

Adlayer core-level shifts of admetal monolayers on transition metal substrates and their relation to the surface chemical reactivity

Using density-functional-theory we study the electronic and structural properties of a monolayer of Cu on the fcc (100) and (111) surfaces of the late 4d transition metals, as well as a monolayer of Pd on Mo bcc(110). We calculate the ground states of these systems, as well as the difference of the ionization energies of an adlayer core electron and a core electron of the clean surface of the adlayer metal. The theoretical results are compared to available experimental data and discussed in a simple physical picture; it is shown why and how adlayer core-level binding energy shifts can be used to deduce information on the adlayer's chemical reactivity.Comment: RevTeX, 7 pages, 2 figure